On pathwise quadratic variation for cadlag functions
Probability
2019-05-07 v3 Classical Analysis and ODEs
Abstract
We revisit H. Foellmer's concept of quadratic variation of a cadlag function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of cadlag processes, one must reformulate the definition of pathwise quadratic variation as a limit in Skorokhod topology of discrete approximations along the partition. One then obtains a simpler definition of quadratic variation which implies the Lebesgue decomposition as a result, rather than requiring it as an extra condition.
Cite
@article{arxiv.1806.07290,
title = {On pathwise quadratic variation for cadlag functions},
author = {Henry Chiu and Rama Cont},
journal= {arXiv preprint arXiv:1806.07290},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1704.00654